Only place I found open for Sunday morning coffee and breakfast was by the yacht club. Cru Cafe has a largish private room upstairs, and their food is excellent.
Name of that place is The Marina Variety Store. It is above Salty Mikes. Best breakfast joint in Charleston for hours, quick service, good food. There is a reason that locals eat there.
And they have a separate room that can be closed off for a private gathering. Just call ahead and give them fair warning. Fleet Landing has made a nice comeback and could accommodate your crowd.